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PRIVACY-PRESERVING RELEASES OF SOCIAL NETWORKS
Chih-Hua Tai
Dept. of CSIE, National Taipei University, New Taipei City, Taiwan
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DATA MINING
The primary task in data mining: development of models about aggregated data. Finding frequent patterns Finding rules
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FINDING PATTERNS
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FINDING RULES
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DATA MINING VS. PRIVACY
The primary task in data mining: development of models about aggregated data. Finding frequent patterns Finding rules
Can we develop accurate models without access to precise information in individual data records? Why?
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PRIVACY ISSUES IN DATA
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PRIVACY ISSUES IN DATA
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PRIVACY ISSUES IN DATA
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DATA MINING AND PRIVACY
The primary task in data mining: development of models about aggregated data.
Can we develop accurate models without access to precise information in individual data records?
Answer: yes, by randomization. R. Agrawal, R. Srikant “Privacy Preserving Data
Mining,” SIGMOD 2000 How about the data utility?
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DATA MINING VS. SOCIAL NETWORKS
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Attributes: Name, Salary, …
Links: Friends, Neighborhood, …
Communities: Interests, Activities, …
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PRIVACY ISSUES ON SOCIAL NETWORKS
Personal information leaked, even if the vertex identifies are hidden…
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Many information can be used to re-associate the vertex with its identity.
Vertex degree: k-degree anonymity , …
Neighborhood configuration: k-neighborhood anonymity, k-automorphism anonymity, k-isomorphism anonymity, grouping-and- collapsing, …
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13
C.-H. Tai, P. S. Yu, D.-N. Yang and M.-S. Chen, "Privacy-preserving Social Network Publication Against Friendship Attacks," In KDD, 2011.
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FRIENDSHIP ATTACK
Still there are another type of information for vertex re-identification – friendship attack
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FRIENDSHIP ATTACK
Given a target individual A and the degree pair information D2 = (d1,d2), a friendship attack (D2,A) exploits D2 to identify a vertex v1 corresponding to A in a published social network where v1 connects to another vertex v2 with the degree pair (dv1
,dv2) = (d1,d2).
15
10
1 2 3
4 5
Alice
6 7
9
8
Ex 1. Assume that an attacker knows that Alice has 3 connections, Bob has 2 connections, and Alice and Bob are friends. The attacker identifies v9 as Alice with 100% confidence.
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FRIENDSHIP ATTACK
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In DBLP data set, the percentages of vertices that can be re-identified with a probability larger than 1/k by degree and friendship attacks.
Original Social Network
k-degree anonymized Social Network
kDegree Attack Friendship Attack Friendship Attack
5 0.28% 5.37% 2.89%
10 0.53% 10.69% 4.65%
15 0.73% 14.71% 5.82%
20 0.93% 18.44% 7.23%
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NEW PRIVACY MODEL AGAINST FRIENDSHIP ATTACK
k2-degree AnonymityA social network is k2-degree anonymous
if, for every vertex with an incident edge of degree pair (d1,d2), there exist at least k − 1 other vertices, each of which also has an incident edge of the same degree pair.
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10
1 2 3
4 5
6 7
9
8
Ex 2. Even with the knowledge (D2,A)=((3,2),Alice), the probability that an attacker can re-identify Alice in the 22-degree anonymous social network is limited to ½.
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THE ANONYMIZATION
Problem formulation: Given a graph G(V, E) and an integer k, the problem is to
anonymize G to satisfy k2-degree anonymity such that information distortion is minimized.
The challenges: Any alteration on an edge will affect the degrees of
two vertices.
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GRAPH ANONYMIZATION ALGORITHMS
Integer Programming formulation Obtain the optimal solution with bad scalability
DEgree SEqence ANonymization (DESEAN) Step1. Degree Sequence Anonymization.
- determine the groups of vertices protecting each others
Step2. Privacy Constraint Satisfaction.- eliminate the advantage of knowing friendship information
Step3. Anonymous Degree Realization.- have the vertices in the same group share the same vertex degree 19
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Step1. Degree Sequence Anonymization. Cluster vertices with similar degrees and select a
target degree dx for each cluster x s. t. each cluster contains at least k vertices and the weighted degree difference ω Σvϵx (dx - d v) + (1 − ω) Σvϵx (d v - dx) is as small as possible.
ALGORITHM DESEAN
20
10
1 2 3
4 5
6 7
9
8
Ex 3. Given k = 2 and ω = 0.5.
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ALGORITHM DESEAN
Step1. Degree Sequence Anonymization. Cluster vertices with similar degrees and select a
target degree dx for each cluster x s. t. each cluster contains at least k vertices and the weighted degree difference ω Σvϵx (dx - d v) + (1 − ω) Σvϵx (d v - dx) is as small as possible.
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10
1 2 3
4 5
6 7
9
8
10
1 2 3
4 5
6 7
9
8
Ex 3. Given k = 2 and ω = 0.5.
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Step2. Privacy Constraint Satisfaction. Add or delete edges between clusters to ensure
that, for each pair of clusters (x,y), the number of vertices in x directly connected to the vertices in y is either zero or not less than k.
ALGORITHM DESEAN
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10
1 2 3
4 5
6 7
9
8
Ex 3. Given k = 2 and ω = 0.5.
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Step2. Privacy Constraint Satisfaction. Add or delete edges between clusters to ensure
that, for each pair of clusters (x,y), the number of vertices in x directly connected to the vertices in y is either zero or not less than k.
ALGORITHM DESEAN
23
10
1 2 3
4 5
6 7
9
8
10
1 2 3
4 5
6 7
9
8
Ex 3. Given k = 2 and ω = 0.5.
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Step3. Anonymous Degree Realization. Adjust edges in G s. t. the vertices in each
cluster x meet the target degree dx selected in Step 1.
10
1 2 3
4 5
6 7
9
8
ALGORITHM DESEAN
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Ex 3. Given k = 2 and ω = 0.5.
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Step3. Anonymous Degree Realization. Adjust edges in G s. t. the vertices in each
cluster x meet the target degree dx selected in Step 1.
10
1 2 3
4 5
6 7
9
8
10
1 2 3
4 5
6 7
9
8
ALGORITHM DESEAN
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Ex 3. Given k = 2 and ω = 0.5.
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C.-H. Tai, P. S. Yu, D.-N. Yang, and M.-S. Chen, ”Structural diversity for privacy in publishing social networks,” In SDM, 2011.
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COMMUNITY IDENTIFICATION
Vertex identification is considered to be an important privacy issue in publishing social networks. ◦ k-degree anonymity, k-neighborhood anonymity, …
In addition to a vertex identity, each individual is also associated with a community identity. ◦ Could be used to infer the political party affiliation or disease
information sensitive to the public.◦ Is a kind of structural information
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COMMUNITY IDENTIFICATION
Community information is explicitly given:
Ex.
Alice knows recently… Bob is sick Bob participates in this social network Bob makes 5 friends. (vertex degree attack)
Bob has AIDS!
AIDS Com. SLE Com.
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COMMUNITY IDENTIFICATION
Community information is not given:
Ex.
Alice knows Bob participates in this social network and has 5 friends. (vertex degree attack)
Alice can know the approximation of Bob’s neighborhood.
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COMMUNITY IDENTIFICATION
% of vertices violating k-structural diversity◦ (a) DBLP◦ (b) ca-CondMat
k-degree anonymization is insufficient 30
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COMMUNITY IDENTIFICATION
structural diversity◦ (a) original DBLP◦ (b) 10-degree anonymized DBLP
Vertices with large degrees appear in a small set of communities 31
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NEW PRIVACY MODEL AGAINST COMMUNITY IDENTIFICATION
k-Structural Diversity To protect against vertex degree attack, for each vertex, there
should be other vertices with the same degree located in at least k-1 other communities.
If a graph satisfies k-structural diversity, then it also satisfies k-degree anonymity.
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THE ANONYMIZATION
Problem formulation: Given a graph G(V, E, C) and an integer k, 1 k |C|, the ≦ ≦
problem is to anonymize G to satisfy k-structural diversity such that information distortion is minimized.
The challenges: How to preserve community structures, even in
the implicit cases, while preserving privacy.
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PROBLEM FORMULATION
Operation Adding Edge ◦ Connect two vertices belonging to the same community.◦ Can avoid destroying the communities.
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PROCEDURE MERGENCE
◦ To protect a vertex v in an existing anonymous group, in which all the vertices have the same degree d
Com. 1
v
Com. 2
Com. 335
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PROCEDURE MERGENCE
◦ To protect a vertex v in an existing anonymous group, in which all the vertices have the same degree d
Com. 1
v
Com. 2
Com. 336
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PROCEDURE CREATION
To create a new anonymous group for a vertex v, such that all the vertices in the group locate in at least k difference communities and have the same degree as v
Com. 1 Com. 2 Com. 3
v
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PROCEDURE CREATION
To create a new anonymous group for a vertex v, such that all the vertices in the group locate in at least k difference communities and have the same degree as v
Com. 1 Com. 2 Com. 3
v
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THE EDGE-REDITECTION MECHANISM
◦ Is defined on w, v, x in the same community w: an anonymized vertex v and x : two not-yet-anonymized vertices
◦ Is to replace the edge (w, v) with the edge (w, x)
v w
v w
x
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THE EDGE-REDITECTION MECHANISM
By mergence
v w
Com. 1 Com. 2
Com. 3
Q. Why needs the Edge-Reditection mechanism?
By mergence
v w
Com. 1 Com. 2
Com. 3
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THE EDGE-REDITECTION MECHANISM
By creation
Com. 1
Com. 2 Com. 3
v w
Q. Why needs the Edge-Reditection mechanism?
By creation
Com. 1
Com. 2 Com. 3
v w
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ALGORITHM EDGECONNECT (EC)
Procedures Mergence and Creation◦ Let Rv be the set of edges that could be redirected away from v
The Edge-Reditection mechanism
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PROBLEM FORMULATION
Operation Adding Edge ◦ Connect two vertices belonging to the same community.◦ Can avoid destroying the communities.
Operation Splitting Vertex◦ Replace a vertex v with a set of substitute vertices, such that
each substitute vertex is connected with at least one edge incident to v originally.
◦ Each substitute vertex presents partial truth of the vertex v.
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PROCEDURE CREATIONBYSPLIT
Split a set of vertices, including v, to create a new anonymous group
Com. 1 Com. 2
Com. 3
v
Com. 1 Com. 2
Com. 3
v1v2
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PROCEDURE MERGEBYSPLIT
Split v into a set of substitute vertices s.t. each substitute vertex is protected in some existing anonymous group
Com. 1 Com. 2
Com. 3 v
v1
v2
v3
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C.-H. Tai, P.-J. Tseng, P. S. Yu and M.-S. Chen, "Identities Anonymization in Dynamic Social Networks," In ICDM-11, 2011.
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THE PROBLEM IN DYNAMIC SCENARIOS…
A dynamic social network will be sequentially released.
An attacker can monitor a victim for a period w.
Therefore, the adversary knowledge includes: The releases G t-w+1,
G t-w+2, …, G t during w A degree sequence Δv
w=(dvt-
w+1, dv
t-w+2, …, dvt) of a victim v
during w47
G2G1
Ex. John has two friends at time 1, and three friends at time 2.
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PRIVACY MODEL: KW-STRUCTURAL DIVERSITY ANONYMITY
Base case of w=1 A group θd, consisting of all
vertices of degree d, is a k-shielding group if there is a vertex subset θ ⊆ θd s. t. (1) |θ |≥ k, and (2) any two vertices u and v in θ,
Cv ∩ Cv = ø, where C is the community identity.
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The adversary knowledge includes: 1. The release
social network G t 2. A degree
sequence Δv
1=(dvt) of a
victim v
Ex. Mary has four friends.
???
G
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PRIVACY MODEL: KW-STRUCTURAL DIVERSITY ANONYMITY
Dynamic scenarios of w>1 A consistent group ΘΔ is the set of vertices
that always share the same degree during w.
A consistent group ΘΔ is a k-shielding if
at each time instant t in w, there is a vertex subset Θ t
⊆ ΘΔ s. t. (1) |Θ t |≥ k, and (2) any two vertices u and v in Θ t, Cv
t ∩ Cv t = ø, where
C t is the community identity at time t.
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The adversary knowledge of includes: 1. The releases G t-
w+1, G t-w+2, …, G t during w
2. A degree sequence Δv
w=(dvt-w+1, dv
t-
w+2, …, dvt) of a
victim v during w
…
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THE ANONYMIZATION
Problem formulation: Suppose that every vertex in a series of sequential
releases G t-w+1, G t-w+2, …, G t-1 is protected. Given G t-w+1, G t-w+2, …, G t-1 and k, anonymize the
current social network Gt s. t. every vertex is protected in a k-shielding consistent group.
The challenges: The anonymization is depended on not only the
current social network but also previous w-1 releases.
Searching through all the w-1 releases to eliminate privacy leak is time consuming.
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ANONYMIZATION ALGORITHM
Construct CS (Clustering Sequence) -Table to prevent the search through w graphs.
CS-Table Summary the vertex information in w-1 previous
releases. Fetch v’ info. in w graphs without scanning the graphs.
According to the degree sequence during w, sort the vertices in hierarchical clustering manner. Vertices in the same k-consistent shielding group are close in CS-Table. CS-Table can be incrementally updated.
According to the vertex ranking in CS-Table, anonymize each vertex to be protected.
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THANK YOU~!